DTIC ADA511757: Effect of Compositional Short Range Order on Glass Formation in Binary Metallic System

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by  Defense Technical Information Center

Effect of Compositional Short Range Order on Glass Formation in Binary Metallic System

Hao Chen, Mahadevan Khantha and Takeshi Egami
Department of Materials Science and Engineering, University of Pennsylvania
Philadelphia, Pa 19104-6272, U.S.A.

ABSTRACT

Molecular Dynamics simulation was carried out to study the glass transition and crystal-
lization in the metal-metalloid binary system with pair-wise potentials. The results show that a
repulsive potential between metalloid (small) atoms increases the glass forming ability. The ob-
servation is consistent with the recent theory of bulk metallic glass formation through local glass
transition and nano-glass formation. The theory predicted that the compositional short-range or-
der (CSRO) prevents the small atom pairing so as to increase the glass forming ability (GFA).
The present results demonstrate the important role of CSRO in bulk metallic glass formation.

INTRODUCTION

The recent development of bulk metallic glass has drawn tremendous interest in both
technological applications and fundamental research of metallic glasses. Since Duwez [1] fabri-
cated the first amorphous metallic alloy Au Si by using the rapid solidification technique in
75 25
1959, the glass forming ability has been greatly improved, seen from the critical cooling rate in-
creasing from 106 K/s to 1 K/s. It has been found that various factors, such as the atomic size ra-
tio, composition, and interatomic potential, affect the GFA of metallic systems, while the under-
ling microscopic mechanism of how to improve GFA remains a major challenge in theoretical
research. Recently, Egami [2] proposed a theory of bulk metallic glass formation based on the
idea of local glass transition. This theory suggests that GFA is improved if the glass transition
does not take place at a single temperature for bulk metallic glasses and there are series of local
glass transitions, which are distributed over a wide temperature range. The GFA depends on the
width of the temperature range, which can be enlarged by introducing large size difference ratio
and CSRO. In this paper, we describe the results of molecular dynamics simulation which prove
that the presence of CSRO improves the GFA of metallic systems.

COMPUTATION PROCEDURE

We performed constant number, pressure and temperature (NPT) molecular dynamics
simulation on a binary AB system composed of 500 particles, 400 “A” and 100 “B” atoms repre-
senting a metal-metalloid binary system. We cooled the system from 1800 K to 600K at a cool-
ing rate of 2 × 1013 K/s. The time step is 1 × 10-3 ps, and 5 × 104 steps are used for equilibrating
the system and additional 5 × 104 steps for collecting the data of interest. Since the purpose of
this study is to examine the general principles of the atomic size effect and not to simulate any
particular alloy, simple model potentials were used to describe the system. The transition metal
atom “A” has the atomic size and mass of iron atom, and the modified Johnson’s potential is used
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Effect of Compositional Short Range Order on Glass Formation in
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Standard Form 298 (Rev. 8-98)
Prescribed by ANSI Std Z39-18
to describe its interaction. The metalloid atom “B” has the same mass as “A”, but a smaller size.
The size scaled modified Johnson’s potential is used to describe the A-B interaction. The B-B in-
teraction is described by two different schemes, the modified Johnson’s potential [3,4] or a de-
creasing exponential potential, which introduces the CSRO.

RESULTS

Figure 1 shows the potentials we used for describing the binary system without CSRO:
The modified Johnson’s potential for A-A, and the size scaled modified Johnson’s potential for
both A-B and B-B, keeping the depth constant. Under this potential scheme, we changed the size
difference ratio of “A” and “B” atoms in the metallic system to study the transition in the quench-
ing process. Figure 2 is the volume change of the system with temperature. For the system with
the size difference ratio of 10% and 12%, the volume has a jump at temperatures of 1250 K and
1125 K, respectively. The discontinuous volume change is a sign of crystallization. The crystalli-
zation temperature becomes lower when the size difference ratio is increased. For the two sys-
tems with larger size difference ratio of 14% and 15%, the volume change is continuous. The
glass transition is not a real phase transition, so volume change is continuous in quenching. The
kink in the volume curve indicates the glass transition. The system with a 15% size difference
ratio has an apparent glass transition at 1050 K, and that with a 14% at 900 K. Figure 3 is the
RDF for the systems with 14% and 12% size difference ratios at 1800K, showing the system is
completely melted. Figure 4 shows that the RDFs of the two systems at 600K are obviously dif-
ferent at the second peak. For the system with a 14% size difference ratio, the second peak is
well separated into two sub-peaks, which are corresponding to the second and third nearest
neighbors of the BCC Fe structure. For the system with a 12% size difference ratio, the second
peak has a small split, which indicates the characteristics of glass. The simulation of 13% size
difference ratio system shows that glass transition and crystallization happen without reproduci-
bility. Thus the critical size difference for glass formation determined by this simulation is 13%.

1.6
14.0 15%
1.2
14%
B-B A-BA-A m] 13.5 12%
U [eV] 00..48 3m [Å/ato 13.0 10%
ato 12.5 Tg=1050K
0.0 er Tg=900K
e p 12.0
-0.4 m
1.5 2.0 R2. 5[Å] 3.0 3.5 olu 11.5 Tc=1250K
V T=1125K
c
11.0
500 1000 1500 2000
Figure 1. Modified Johnson's potential on
Temperature [K]
A-A, and Sized scaled Johnson's potential
for A-B and B-B (No compositional short
Figure 2. Volume change with temperature for metal-
range order).
lic systems with different size ratio.
7
7
6 14% 6 14%
12%
12%
5
5
4
4
F
D 3 F
R D 3
R
2
2
1
1
0
0
0 2 4 6 8 10
0 2 4 6 8 10
R[Å]
R[Å]
Figure 3. RDF indicating liquid structure for the Figure 4. RDF indicating a crystal structure for 12%
system with 14% and 12% size difference ratios size difference ratio and a glass structure for 14%
size difference ratio. (No compositional short range
order)

14.0
W/O CSRO
1.6
m] 13.5 W/ CSRO
o
at
1.2 3Å/ 13.0
A-A A-B B-B m [ Tg=1000K
V] 0.8 ato 12.5
U [e 0.4 e per 12.0
m
u
0.0 ol 11.5
V
T=1125K
c
-0.4 11.0
1.0 1.5 2.0 2.5 3.0 3.5 4.0 500 1000 1500 2000
R [Å] Temperature [K]
Figure 5. Modified Johnson's potential for A-
Figure 6. Volume change with temperature for the system
A, and sized scaled Johnson's potential for A-
with a 12% size difference ratio (glass transition with
B and repulsive exponential for B-B. (Compo-
CSRO, crystallization without CSRO).
sitional short range order exists)

In order to study the effects of the CSRO, we introduced a repulsive exponential potential
on B-B pair. This potential produces a very strong repulsive force between the B-B first nearest
neighbors, so it can prevent a contact of B and B atoms. Figure 5 is the potentials we used in de-
scribing the atomic interaction. The interactions for A-A and A-B are the same as before, and only
the B-B interaction is changed. As shown above the binary system without CSRO crystallizes at
the cooling rate of 2 × 1013 K/s when the size difference is 12%. However, after the CSRO is in-
troduced a glass transition occurs. Figure 6 is the volume change with the temperature of the me-
tallic system before and after introducing the chemical short-range order. The volume has a con-
tinuous change with temperature with the presence of the CSRO, which indicates a glass transi-
tion, with the glass transition temperature of 1000 K. Figure 7 shows the RDF at 600 K for the
two metallic systems. The clear difference in the split of the second peak indicates that different
transitions take place in the quenching process.

DISCUSSION

The critical size difference for glass formation for the system without CSRO, 13 %, cor-
respond to the volume ratio of ∆V/<V> = 0.367, where ∆V = V – V , <V> = C V + C V , V
A B A A B B A
and V are the atomic volume for A and B, and C and C are the atomic compositions of A and B.
B A B
This gives the size ratio factor,

∆V
Cmin =0.073 , (1)
B V

where C min is the minimum concentration of B element for glass formation, rather than 0.1 for
B
the experimental and theoretical size factor [5]. This must be due to the rapid cooling rate of the
simulation. Generally, the higher the cooling rate the more stable glasses are. As stated by D.
Turnbull, any material becomes a glass if it is cooled from the liquid state fast enough [6]. Thus
this much of underestimate of the critical alloy composition/size difference is not surprising. This,
however, is the most critical shortcoming of the MD simulation in evaluating the GFA. The MD
simulation can provide insights and trends, but not quantitative information as far as GFA is con-
cerned.
The effect of the CSRO introduced by applying the repulsive exponential potential on
small B-B atoms is to prevent the B-B pairs. Figure 8 is the partial RDF of “B” atoms at 600 K
with the repulsive potential and the size scaled modified Johnson’s potential. Under the repulsive
potential, there is no first nearest neighbor of B-B atoms, which means “B” atom is surrounded
only by “A” atoms. The volume and RDF evolution with temperature show that the existence of
the CSRO helps glass transition over the crystallization.

7
W/O CSRO
6
W/O CSRO 1.0 W/ CSRO
W/ CSRO
5
4
F F
RD 3 RD 0.5
2
1
0.0
0
0 2 4 6 8 10 0 2 4 6 8 10
R[Å] R[Å]
Figure 7. RDF at 600K for the system with a 12% Figure 8. Partial RDF of B atom at above melting
size difference ratio (glass transition with CSRO, crys- temperature (no B-B nearest neighbor with CSRO)
tallization without CSRO)
Egami [7] proposed the method of describing the glass transition in metallic glass in
terms of the fluctuation in the local stresses. The glass transition is defined as the percolation of
the locally collapsed atomic environments, and T is given by,
g

2ΩK ΩK
T = (εcrit)2 = 6.14×10−3 , (2)
g k V k
B B

where Ω is atomic volume, K is the bulk modulus, k is the Boltzmann constant, and ε crit is the
B v
critical volume expansion for local topological stability. For the present system equation (2)
gives T = 591 K, using the average values of Ω and K, which is lower than the glass transition
g
temperature observed by the simulation. The fast cooling rate is the reason why the two glass
transition temperatures are inconsistent.
This theory was further extended and recently applied to the question of bulk metallic
glass formation [2]. A novel concept of local glass transition was introduced, taking note that the
topological instability condition that leads to equation (2) can be defined locally. In the binary
metallic system, there are four local structure collapses: an “A” atom centered local structure
broken by insertion of an “A” atom, an “A” atom centered local structure broken by insertion of
a “B” atom, a “B” atom centered local structure broken by insertion of an “A” atom, and a “B”
atom centered local structure broken by insertion of an “A” atom. Thus four different local glass
transitions can be defined correspond to each scenario. It was found that if the formation of pairs
made of two small atoms is prevented, the local glass transition temperature for a small atom is
higher than that for a large atom, when ΩK is equal. This means that the local environment of a
small atom freezes earlier than large atoms during the process of quenching, so the diffusion of
the system is suppressed, increasing the viscosity, making crystallization more difficult, and thus
improving GFA.
The present simulation confirms this prediction. Without the CSRO the critical size dif-
ference for the solute concentration of 0.2 was 13 %. With the CSRO, however, the system with
the size factor of 12 % was vitrified, proving the improvement in GFA. Work is in progress to
determine the critical size difference with the CSRO.

CONCLUSIONS

This paper shows that by simply introducing compositional short-range order, the glass
forming ability of metallic system is improved. The simulation results can be explained by the
recent theory of bulk metallic glass formation through local glass transition and nano-glass for-
mation. The prevention of small and small atomic pairs will result in the increase of the glass
transition temperature of the system. The results provide a useful guidance of the selection of
new bulk metallic glass.

ACKNLOWLEDGMENTS

This work was supported by the Defense Advanced Research Projects Agency and the
Office Naval Research through DARPA/ONR Grant N00014-01-1-0961 and through Boeing Co.
Grant 44955-00-00. The author is grateful to S. J. Poon, G. S. Shiflet and W. L. Johnson for use-
ful discussions.
REFERENCES

1) Clement, W., Willens, R. H., and Duwez, P., Nature 187, 869 (1960).
2) Egami, T., Mater. Trans., 43, 510 (2002).
3) Johnson, R.A., Phys. Rev. A 34, 1329 (1964).
4) Egami, T. and Srolovitz, D, J. Phys. F, 12, 2414 (1982).
5) Egami, T. and Waseda, J. Non-Cryst. Solids, 64, 113 (1984).
6) Turnbull, D., Contemp. Phys., 10, 473 (1969).
7) Egami, T., Mater. Sci. Eng., A226-228, 261 (1997).